Question

Which expression is equivalent to sine (startfraction pi over 12 endfraction) cosine (startfraction 7 pi over 12 endfraction) minus cosine (startfraction pi over 12 endfraction) sine (startfraction 7 pi over 12 endfraction)?

Answer 1

-1

Explanation:

Recall that
`\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(b)`, so if
`a=(\pi)/(12)` and
`b=(7\pi)/(12)`, then:

`\sin((\pi)/(12))\cos((7\pi)/(12))-\cos((\pi)/(12))\sin((7\pi)/(12))=\sin((\pi)/(12)-(7\pi)/(12))=\sin(-(6\pi)/(12))=\sin(-(\pi)/(2))=-1`